Move the labeled point to any complex number, [math]r\text{ cis }\theta[/math], on the polar grid above.[br][br]The red curve shows all of the powers of that number. To see the first [math]n[/math] powers, click on the checkbox. [br]You can adjust [math]n[/math] from 1 to 20. You can also show the segments from 0 to each point to see the relationship between their arguments.[br][br]Interesting things to explore:[br]1. What happens if [math]r=1[/math]?[br]2. What happens if the number is on the real axis ([math]\theta=0^{\circ}[/math] or [math]\theta=180^{\circ}[/math])?[br]3. What if [math]r<1[/math]?[br]4. What number is always on the red curve, no matter where you drag [math]r\text{ cis }\theta[/math]?[br]